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Angles on the Coordinate Plane (Lesson 9.5)

Learning Targets
  • Draw angles in standard position on the coordinate plane with both positive and negative angle measures.
  • Find coterminal angles for a given angle.
  • Calculate a reference angle for an angle in standard position.
  • Find trigonometric ratios for angles in standard position.
Activity: Wheel of Algebra

Experience First

For today’s lesson, each student will need a copy of the prize spinner and a paper clip to use as a spinner. You’ll notice that the prizes range from real to silly! We’d recommend you change the prizes to reflect you and your students. (Your students probably don’t want beard grooming lessons with Mr. Wilcox!) Begin the lesson by making sure all of the students understand the rules of the spinner. The spinner always starts on the positive x-axis and spins counterclockwise.


After that, students can work through the entire activity in their groups. Have students write their answers on the board as they complete them.

Guiding Questions

  • How many degrees is each sector? How do you know?

  • How many degrees is one full spin around the circle?

  • Can the spinner go around the circle more than one time? 

  • Where would the point be located? Let’s draw a triangle using the origin and the point.

  • If we know two sides of a triangle, can we find an angle that goes along with it? How?

Formalize Later

We have a LOT of vocabulary today! Make sure you are properly labeling in the margin notes and continue to model the correct usage whenever possible. Students will probably struggle with the last Check Your Understanding problem. As you’re helping groups, make sure to draw their attention to proper labeling. They should label their angle with sigma and the reference angle with sigma prime. This can be confusing for students so make sure to save some time at the end of the lesson to go over this.


In later lessons, we found it helpful to remind students that the reference angle shows how far you are from the free spin (x-axis).

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